Chapter 1

Data Storage

2

Chapter 1: Data Storage 1.1 Bits and Their Storage 1.2 Main Memory 1.3 Mass Storage 1.4 Representing Information as

Bit Patterns 1.5 The Binary System 1.6 Storing Integers

3

Chapter 1: Data Storage (continued)

1.7 Storing Fractions 1.8 Data Compression 1.9 Communications Errors

4

Bits and their meaning Bit = Binary Digit = a symbol

whose meaning depends on the application at hand.

Some possible meanings for a single bit Numeric value (1 or 0) Boolean value (true or false) Voltage (high or low)

5

Bit patterns All data stored in a computer are

represented by patterns of bits: Numbers Text characters Images Sound Anything else…

6

Boolean operations Boolean operation = any operation

that manipulates one or more true/false values Can be used to operate on bits

Specific operations AND OR XOR NOT

7

Figure 1.1 The Boolean operations AND, OR, and XOR (exclusive or)

8

Gates Gates = devices that produce the

outputs of Boolean operations when given the operations’ input values Often implemented as electronic

circuits Provide the building blocks from

which computers are constructed

9

Figure 1.2 A pictorial representation of AND, OR, XOR, and NOT gates as well as their input and output values

10

Flip-flops Flip-flop = a circuit built from

gates that can store one bit of data. Has an input line which sets its stored

value to 1 Has an input line which sets its stored

value to 0 While both input lines are 0, the most

recently stored value is preserved

11

Figure 1.3 A simple flip-flop circuit

12

Figure 1.4 Setting the output of a flip-flop to 1

13

Figure 1.4 Setting the output of a flip-flop to 1 (cont’d)

14

Figure 1.4 Setting the output of a flip-flop to 1 (cont’d)

15

Figure 1.5 Another way of constructing a flip-flop

16

Other storage techniques Dynamic memory – must be replenished

periodically – Example: capacitors Volatile memory – holds its value until the

power is turned off – Example: flip-flops Non-volatile memory – holds its value after

the power is off – Example: magnetic storage Read-only memory (ROM) – never changes –

Examples: flash memory, compact disks

17

Hexadecimal notation Hexadecimal notation = a shorthand

notation for streams of bits. Stream = a long string of bits. Long bit streams are difficult to make sense

of. The lengths of most bit streams used in a

machine are multiples of four. Hexadecimal notation is more compact.

Less error-prone to manually read, copy, or write

18

Figure 1.6 The hexadecimal coding system

19

Main memory: cells Cells = manageable units (typically 8 bits) into

which a computer’s main memory is arranged. Byte = a string of 8 bits. High-order end = the left end of the

conceptual row in which the contents of a cell are laid out.

Low-order end = the right end of the conceptual row in which the contents of a cell are laid out. Least significant bit = the last bit at the low-order

end.

20

Figure 1.7 The organization of a byte-size memory cell

21

Main memory addresses Address = a “name” to uniquely identify

one cell in the computer’s main memory The names for cells in a computer are

consecutive numbers, usually starting at zero

Cells have an order: “previous cell” and “next cell” have reasonable meanings

Random Access Memory = memory where any cell can be accessed independently

22

Figure 1.8 Memory cells arranged by address

23

Measuring memory capacity: Not quite like the metric system

“ Kilo-” normally means 1,000;Kilobyte = 210 = 1024

“Mega-” normally means 1,000,000;Megabyte = 220 = 1,048,576

“Giga-” normally means 1,000,000,000;Gigabyte = 230 = 1,073,741,824

24

Mass Storage Systems Non-volatile; data remains when computer

is off Usually much bigger than main memory Usually rotating disks

Hard disk, floppy disk, CD-ROM Much slower than main memory

Data access must wait for seek time (head positioning) Data access must wait for rotational latency

25

Figure 1.9 A disk storage system

26

Figure 1.10 CD storage format

27

Figure 1.11 A magnetic tape storage mechanism

28

Files File = the unit of data stored on a mass

storage system. Logical record and Field = natural groups

of data within a file Physical record = a block of data

conforming to the physical characteristics of the storage device.

Buffer = main memory area sometimes set aside for assembling logical records or fields of a file

29

Figure 1.12 Logical records versus physical records on a disk

30

Figure 1.13 The message “Hello.” in ASCII

31

Representing text Each printable character (letter,

punctuation, etc.) is assigned a unique bit pattern. ASCII = 7-bit values for most symbols

used in written English text Unicode = 16-bit values for most

symbols used in most world languages today

ISO proposed standard = 32-bit values

32

Representing numeric values Binary notation – uses bits to

represent a number in base two Limitations of computer

representations of numeric values Overflow – happens when a number is

too big to be represented Truncation – happens when a number is

between two representable numbers

33

Figure 1.14 The sound wave represented by the sequence 0, 1.5, 2.0, 1.5, 2.0, 3.0, 4.0, 3.0, 0

34

Figure 1.15 The base ten and binary systems

35

Figure 1.16 Decoding the binary representation 100101

36

Figure 1.17 An algorithm for finding the binary representation of a positive integer

37

Figure 1.18 Applying the algorithm in Figure 1.15 to obtain the binary representation of thirteen

38

Figure 1.19 The binary addition facts

39

Figure 1.20 Decoding the binary representation 101.101

40

Representing Integers Unsigned integers can be

represented in base two Signed integers = numbers that

can be positive or negative Two’s complement notation = the

most popular representation Excess notation = another less

popular representation

41

Figure 1.21 Two’s complement notation systems

42

Figure 1.22 Coding the value -6 in two’s complement notation using four bits

43

Figure 1.23 Addition problems converted to two’s complement notation

44

Figure 1.24 An excess eight conversion table

45

Figure 1.25 An excess notation system using bit patterns of length three

46

Figure 1.26 Floating-point notation components

47

Figure 1.27 Coding the value 25⁄8

48

Figure 1.28 Decompressing xyxxyzy (5, 4, x)

49

Figure 1.29 The ASCII codes for the letters A and F adjusted for odd parity

50

Figure 1.30 An error-correcting code

51

Figure 1.31 Decoding the pattern 010100 using the code in Figure 1.30